1. Technical Field
The present invention relates to a measuring apparatus, a test apparatus, a recording medium, a program and an electronic device. More particularly, the present invention relates to a measuring apparatus for measuring jitter of a signal under measurement, and to a measuring apparatus for measuring jitter generated by an AD converter.
2. Related Art
One of the methods to measure jitter generated by an AD converter is to input an input signal and a sampling clock into the AD converter and measure jitter included in the output from the AD converter. Here, the input signal is a sine wave with small jitter, for example, and the sampling clock also has small jitter. The jitter generated by the AD converter represents, for example, the variance in the aperture delay from the zero cross timing of the sampling clock at which a start conversion command is given to the moment at which the level of the input signal is held. This jitter is also referred to as aperture jitter.
The aperture jitter indicates the random variation in the time required to hold an analog input. Accordingly, the aperture jitter is considered to be one type of instantaneous phase noise.
The sampling clock supplied to a high-resolution AD converter has very small jitter, that is to say, phase noise. For example, the jitter is −140 dBc/Hz when the offset frequency is equal to 100 kHz. This necessitates expensive special measuring equipment for the measurement. Therefore, there is a demand for a method and an apparatus which can accurately measure the sampling clock with very small jitter at a low cost.
The jitter contained in the output from the AD converter may be measured based on the spectrum obtained by performing Fourier transform on the output discrete waveform from the AD converter. For example, the root mean square (RMS) value of the jitter and the signal to noise ratio, SNR, are estimated based on the energy of the noise component contained in the spectrum.
The SNR is defined as the ratio of signal power to noise power. The signal power and the noise power are measured with respect to the observable positive frequencies. The noise that may be generated by the AD converter 400 includes quantization noise, aperture jitter and thermal noise. Such varieties of noise degrade the SNR.
The SNR due to the quantization noise and the aperture jitter, and the sampling clock jitter, generated by the AD converter is represented by the following equation.
                    SNR        =                  10          ⁢                      log            10                    ⁢                                    {                                                                    (                                                                  V                        FS                                            2                                        )                                    2                                                                                            Δ                      2                                        12                                    +                                                                                    (                                                                              V                            FS                                                    2                                                )                                            2                                        ⁢                                                                  (                                                  2                          ⁢                          π                          ⁢                                                                                                          ⁢                                                      f                                                          i                              ⁢                                                                                                                          ⁢                              n                                                                                                      )                                            2                                        ⁢                                          σ                      Δϕ                      2                                                                                  }                        ⁡                          [              dB              ]                                                          Equation        ⁢                                  ⁢        1            Here, VFS/2 denotes the amplitude of the analog sine wave input into the AD converter, fin denotes the frequency of the sine wave, Δ denotes the quantization step of the AD converter, and σΔφ denotes the aperture jitter.
As seen from the equation 1, when the sine wave input into the AD converter has a sufficiently low frequency, the SNRQ is dominated by the quantization noise. In other words, the equation 1 becomes the following equation indicating a constant value.
                                                                        SNR                →                                  SNR                  Q                                            =                              10                ⁢                                  log                  10                                ⁢                                  {                                                                                    (                                                                              V                            FS                                                    2                                                )                                            2                                                                                      Δ                        2                                            12                                                        }                                                                                                        =                                                6.02                  ⁢                                      B                    e                                                  +                                  1.76                  ⁢                                                                          [                  dB                  ]                                                                                        Equation        ⁢                                  ⁢        2            
On the other hand, when the frequency fin is sufficiently high and the quantization step is sufficiently small, the SNRT is dominated by the aperture jitter. Accordingly, the equation 1 becomes the following equation. The SNRT linearly changes with respect to the logarithmic frequency log10fin.
      SNR    →          SNR      T        =      10    ⁢          log      10        ⁢                  1                              (                          2              ⁢              π              ⁢                                                          ⁢                              f                                  i                  ⁢                                                                          ⁢                  n                                            ⁢                              σ                Δϕ                                      )                    2                    ⁡              [        dB        ]            Which is to say,SNRT∝−20 log10fin−20 log10 σΔφ  Equation 3
FIG. 28A illustrates, as an example, the relation between the effective number of bits ENOB of the AD converter and the frequency of the analog input which is applied into the AD converter. As stated earlier, the ENOBQ remains at a substantially constant value in the region where the analog input has a low frequency, that is to say, fin<100 MHz. On the other hand, the ENOBT changes linearly in the region where the analog input has a high frequency, that is to say, fin>100 MHz. To calculate the linear change, it is necessary to measure the ENOB at, at least, two frequencies in the region where the analog input has a high frequency.
FIG. 28B illustrates, as an example, the spectra obtained by performing the Fourier transform on the outputs from the AD converter. FIG. 28B shows the spectrum of the discrete waveform data output from the AD converter when a low-frequency input signal is applied to the AD converter, as shown in the left graph in FIG. 28B, and the spectrum of the discrete waveform data output from the AD converter when a high-frequency input signal is applied to the AD converter, as shown in the right graph in FIG. 28B.
Each of the spectra shown in FIG. 28B contains a signal component corresponding to the frequency of the input signal, for example, the component of the line spectrum in FIG. 28B, and a noise component generated by the AD converter, for example, the remaining components in FIG. 28B. Here, the noise component contains therein quantization noise component that is independent from the frequency of the input signal and a jitter component that is dependent on the frequency of the input signal. Therefore, it is assumed that the energy of the jitter component that is dependent on the frequency of the input signal can be obtained by calculating the difference Δ in the energy, that is to say, the sum of the signal component and the noise component, between the spectra, as illustrated in FIG. 28B. This assumption, however, has not been verified.
The ENOB of the AD converter with respect to the amplitude axis can be obtained by calculation based on the quantization noise component. Which is to say, the ENOB can be calculated based on the SNR of the spectrum of the discrete waveform data output from the AD converter when an input signal having a given frequency is input into the AD converter. However, no methods and apparatuses have been known which can measure the ENOB due only to the jitter component.
In order to estimate the jitter by measuring the difference between the spectra as described above, it is required to measure spectra twice. Also, it is not possible to measure the ENOB or SNR for which the aperture jitter is dominant, i.e. the ENOBT or SNRT in the right region in FIG. 28A, by using the analog input having the low frequency as shown in the left region in FIG. 28A
The two spectra illustrated in FIG. 28B are observed at different timings, that is to say, not measured at the same time. Therefore, it is difficult to accurately isolate the jitter component contained in the noise component from the quantization noise component in the noise component. Additionally, since the above method calculates the jitter based on the energies of the noise components contained in the spectra, the above method can only calculate the RMS value of the jitter, but cannot calculate the change in the instantaneous value of the jitter such as the peak value and the peak-to-peak value, and the aperture jitter waveform. Therefore, it is difficult to provide feedback data to the design of the AD converter.
FIG. 29 illustrates a different method to measure the jitter based on the spectrum obtained by performing the Fourier transform on the output from the AD converter. This method extracts, from the spectrum, frequency components within a frequency range which is substantially symmetrical with respect to the fundamental frequency of the input signal and contains no harmonic components, and performs the inverse Fourier transform on the extracted frequency components. In this way, the method generates an analytic signal for the output waveform from the AD converter.
It is important to set, to zero, all of the harmonic components, which are strongly correlated to the signal, in order to measure the random variation in both the amplitude and the timing in the frequency domain. When the harmonic components are all set to zero, the spectrum is left with the line spectrum of the fundamental and the random noise.
Here, the instantaneous phase of the output waveform from the AD converter is obtained by the arctangent of the real and imaginary parts of the analytic signal, and the obtained instantaneous phase can be used to obtain the jitter. This method is disclosed in U.S. Pat. No. 6,525,523, for example.
Obtaining the instantaneous phase of the output waveform, this method can calculate the peak value, the peak-to-peak value and the like of the jitter. Note that performing the Fourier transform on the discrete waveform output from the AD converter produces the spectrum containing the harmonic components as illustrated in the left graph in FIG. 28B. Because of the aliasing effects, the line spectra of the harmonic components are present in the vicinity of the line spectrum of the fundamental. For this reason, when the frequency components that contain no harmonic components are extracted by using a filter in accordance with the method illustrated in FIG. 29, the observable frequency range is narrow and broadband jitter can not be measured.
As explained in the above, the method illustrated in FIG. 29 can not measure the noise component corresponding to the frequency which is far from the fundamental frequency of the input signal. To summarize, there is a demand for a method which can measure the peak value, the peak-to-peak value and the like of the jitter, and can measure jitter in a broad bandwidth. Here, since the conversion rate of the AD converter is expected to further increase, it is preferable to provide a method and an apparatus which can measure the intrinsic jitter component of the AD converter or the ENOB corresponding only to the jitter component of the sampling clock.